Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

From a Game Theoretic Approach to Numerical Approximation and Algorithm Design

Houman Owhadi, Clint Scovel

• Publisher: Cambridge University Press
• Year: 2019
• Print ISBN:
  9781108484367
• eBook ISBN:
  9781108655644
• Topic: Mathematics
• Subtopic: Mathematical Analysis
• Index: Mathematics

Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• Acknowledgments
• Reading Guide
• 1 Introduction
• Part I The Sobolev Space Setting
• Part II The Game Theoretic Approach
• Part III The Banach Space Setting
• Part IV Game Theoretic Approach on Banach Spaces
• Part V Applications, Developments, and Open Problems
• Part VI Appendix
• Bibliography
• Algorithms
• Glossary
• Nomenclature
• Index
• Identities